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Grade 10 Math Courses - Alberta Curriculum

Discover Alberta's Grade 10 math options: Mathematics 10C and 10-3. These courses build foundational skills in algebra, geometry, and problem-solving, preparing students for future academic and career paths.

Mathematics 10C

Mathematics 10-3

Alberta Grade 10 Math Curriculum - Mathematics 10C and 10-3

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LO_ID	Learning Outcome-Skills & Procedures	StudyPug Topic
AB.GO.10C.1	Develop spatial sense and proportional reasoning: Solve problems involving linear measurement, using SI and imperial units of measure, estimation strategies, and measurement strategies. Apply proportional reasoning to problems that involve conversions between SI and imperial units of measure.	Conversions between metric and imperial systems Metric systems Imperial systems Conversions involving squares and cubic Upper and lower bound

AB.GO.10C.2

Develop spatial sense and proportional reasoning: Solve problems involving the surface area and volume of 3-D objects, including right cones, right cylinders, right prisms, right pyramids, and spheres, using SI and imperial units.

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

AB.GO.10C.3

Develop spatial sense and proportional reasoning: Develop and apply the primary trigonometric ratios (sine, cosine, tangent) to solve problems that involve right triangles.

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Other word problems relating angles in trigonometry

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Use tangent ratio to calculate angles and sides (Tan = o / a)

AB.GO.10C.4

Develop algebraic reasoning and number sense: Demonstrate an understanding of factors of whole numbers by determining the prime factors, greatest common factor, least common multiple, square root, and cube root.

Understanding the number systems

Prime factorization

Greatest common factors (GCF)

Least common multiple (LCM)

Square and square roots

Cubic and cube roots

AB.GO.10C.5

Develop algebraic reasoning and number sense: Demonstrate an understanding of irrational numbers by representing, identifying and simplifying irrational numbers, and ordering irrational numbers.

Rational vs. Irrational numbers

Converting repeating decimals to fractions

Converting radicals to mixed radicals

Converting radicals to entire radicals

Adding and subtracting radicals

Multiplying and dividing radicals

Rationalize the denominator

Evaluating and simplifying radicals

AB.GO.10C.6

Develop algebraic reasoning and number sense: Demonstrate an understanding of powers with integral and rational exponents.

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Negative exponent rule

Combining the exponent rules

Scientific notation

Convert between radicals and rational exponents

Solving for exponents

Product rule of exponents

AB.GO.10C.7

Develop algebraic reasoning and number sense: Demonstrate an understanding of the multiplication of polynomial expressions (limited to monomials, binomials and trinomials), concretely, pictorially and symbolically.

What is a polynomial?

Polynomial components

Multiplying monomial by monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Applications of polynomials

AB.GO.10C.8

Develop algebraic reasoning and number sense: Demonstrate an understanding of common factors and trinomial factoring, concretely, pictorially and symbolically.

Common factors of polynomials

Factoring polynomials by grouping

Solving polynomials with unknown coefficients

Solving polynomials with unknown constant terms

Factoring polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

Solving polynomials with the unknown "b" from ax^2 + bx + c

Factoring polynomials: ax^2 + bx + c

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Evaluating polynomials

Using algebra tiles to factor polynomials

Solving polynomial equations

Word problems of polynomials

AB.GO.10C.9

Develop algebraic and graphical reasoning through the study of relations: Interpret and explain the relationships among data, graphs and situations.

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

AB.GO.10C.10

Develop algebraic and graphical reasoning through the study of relations: Demonstrate an understanding of relations and functions.

Distance formula:

d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Parallel and perpendicular lines in linear functions

Applications of linear relations

AB.GO.10C.11

Develop algebraic and graphical reasoning through the study of relations: Demonstrate an understanding of slope with respect to rise and run, line segments and lines, rate of change, parallel lines, and perpendicular lines.

Midpoint formula:

M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)

Slope equation:

m = \frac{y_2-y_1}{x_2- x_1}

Slope intercept form: y = mx + b

General form: Ax + By + C = 0

Point-slope form: y - y_1 = m(x - x_1)

AB.GO.10C.12

Develop algebraic and graphical reasoning through the study of relations: Describe and represent linear relations, using words, ordered pairs, tables of values, graphs, and equations.

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Introduction to linear equations

Introduction to nonlinear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Applications of linear equations

AB.GO.10C.13

Develop algebraic and graphical reasoning through the study of relations: Determine the characteristics of the graphs of linear relations, including the intercepts, slope, domain, and range.

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

AB.GO.10C.14

Develop algebraic and graphical reasoning through the study of relations: Relate linear relations expressed in slope-intercept form (y = mx + b), general form (Ax + By + C = 0), and slope-point form (y - y1 = m(x - x1)) to their graphs.

Factor by taking out the greatest common factor

Factor by grouping

Factoring difference of squares:

x^2 - y^2

Factoring trinomials

Factoring difference of cubes

Factoring sum of cubes

AB.GO.10C.15

Develop algebraic and graphical reasoning through the study of relations: Determine the equation of a linear relation, given a graph, a point and the slope, two points, or a point and the equation of a parallel or perpendicular line, to solve problems.

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Applications of quadratic functions

Quadratic function in vertex form: y = a(x-p)^2 + q

Completing the square

AB.GO.10C.16

Develop algebraic and graphical reasoning through the study of relations: Represent a linear function, using function notation.

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

AB.GO.10C.17

Develop algebraic and graphical reasoning through the study of relations: Solve problems that involve systems of linear equations in two variables, graphically and algebraically.

Combining transformations of functions

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

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